Week 2a Lecture_Utility

Week 2a Lecture_Utility - Week 2 Part I Utility Preferences...

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Unformatted text preview: Week 2 Part I Utility Preferences - A Reminder x y: x is weakly preferred to y. x y: x is strictly preferred to y. x y: x and y are equally preferred. We assume that a preference is complete (reflexive) and transitive. ~ Utility Functions If a preference relation that is additionally continuous can be represented by a continuous utility function . Continuity means that small changes to a consumption bundle cause only small changes to the preference level. Utility Functions A utility function U(x) represents a preference relation if and only if: x x U(x) >= U(x) We get the following for free: x x U(x) > U(x) x x U(x) = U(x). ~ ~ & ~ Utility Functions Utility is an ordinal (i.e. ordering) concept. E.g . if U(x) = 6 and U(y) = 2 then bundle x is strictly preferred to bundle y. But x is not preferred three times as much as is y. If we can find one utility representation, then we have infinitely many. Utility Functions U(x 1 ,x 2 ) = x 1 x 2 (2,3) (4,1) (2,2). Define V = U 2 . Then V(x 1 ,x 2 ) = x 1 2 x 2 2 and V(2,3) = 36 > V(4,1) = V(2,2) = 16 so again (2,3) (4,1) (2,2). V preserves the same order as U and so represents the same preferences. ~ ~ Utility Functions If U is a utility function that represents a preference relation and f is a strictly increasing function, then V = f(U) is also a utility function representing . ~ ~ Utility Functions & Indiff. Curves An indifference curve contains equally preferred bundles. Equal preference same utility level....
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Week 2a Lecture_Utility - Week 2 Part I Utility Preferences...

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